CPI measures a basket of goods and these will differ from country to country. But, let's assume the US government does a good job on estimating the increase in the consumer prices for an average citizen. Still it does not address the problem I mentioned about printing money, which is dissolving the value of money. If that was not true, as I mentioned earlier, we could just print the money and have eternal vacations.
The question is why we do not see the negative effects in the reported CPI. One explanation is a deflationary force that mitigates the inflationary moves. The long term stable deflationary force is an increase in productivity by technological advancements. But I do not think it can keep up with the printing press.